In the top picture, a wire nut that had been burning in the wall is shown. Wire nuts are used to connect copper wires to each other. The copper wires are twisted together to make a splice, so the electricity can flow from one to the next. The splice has to be made up tight and solid. The spliced wires must be wrapped tightly against each other so the electrons can flow from the surface of the first wire to the second wire easily and without resistance. If the splice is poorly made or loose, such that there are air gaps between the wires, the electricity "jumps" through the air from one wire to the other. That is called arcing. When wires arc they overheat and can start a fire, especially with the little "hairs" and frayed-end fibers being in immediate contact, as is found where cloth-covered wire has be deteriorating for generations.
This is very clear in the second picture, as well as the third and forth. In the third picture, two pieces of BX cable with cloth-covered wire can be seen, with the actual wire insulation at the connection point being very frayed and combustible.
The bottom picture shows two more of these BX cables, with the outlet box having been removed.
In the second picture, you can see that the insulation itelf has completely fallen off the hot wire. The bare metal portion is visible just above the red wire nut. This exposed, hot wire could have caused a short-circuit easily. It is not a good idea to overload any old cloth covered wire. Depending on the circuit breaker to disconnect the current flow before a fire can begin is a fallacy. It won't, unless it is an AFCI. Arc-fault circuit breakers have been designed specifically for disconnecting the circuit when they detect even a small arc, which is where many electrical fires begin. Unfortunately, you can not install an AFCI circuit breaker without rewiring first. You could not just connect it to pre-existing wiring unless it has been specially designed to accept it.
I will post again later as this job progresses.